A Multivariate Complexity Analysis of the Material Consumption Scheduling Problem

TL;DR

This paper investigates the computational complexity of a resource-constrained scheduling problem, analyzing how resource supply parameters affect problem tractability, and providing a detailed complexity landscape for the single-machine case.

Contribution

It systematically explores the parameterized complexity of the material consumption scheduling problem, revealing new tractability and intractability results based on resource supply parameters.

Findings

Identifies parameters influencing problem complexity

Provides new tractability results for certain parameter settings

Establishes intractability results for other parameter configurations

Abstract

The NP-hard MATERIAL CONSUMPTION SCHEDULING Problem and closely related problems have been thoroughly studied since the 1980's. Roughly speaking, the problem deals with minimizing the makespan when scheduling jobs that consume non-renewable resources. We focus on the single-machine case without preemption: from time to time, the resources of the machine are (partially) replenished, thus allowing for meeting a necessary pre-condition for processing further jobs, each of which having individual resource demands. We initiate a systematic exploration of the parameterized (exact) complexity landscape of the problem, providing parameterized tractability as well as intractability results. Doing so, we mainly investigate how parameters related to the resource supplies influence the computational solvability. Thereby, we get a deepened understanding of the algorithmic complexity of this fundamental scheduling problem.